数学最新文献_第10页

Soft-neighborhood based robust fuzzy rough sets for semi-supervised feature selection

IF 3.2 1区数学

Fuzzy Sets and Systems Pub Date : 2025-04-01 DOI: 10.1016/j.fss.2025.109397

Shuang An , Yuhang Gong , Changzhong Wang , Ge Guo

{"title":"Soft-neighborhood based robust fuzzy rough sets for semi-supervised feature selection","authors":"Shuang An , Yuhang Gong , Changzhong Wang , Ge Guo","doi":"10.1016/j.fss.2025.109397","DOIUrl":"10.1016/j.fss.2025.109397","url":null,"abstract":"<div><div>Fuzzy rough set (FRS) theory has been widely concerned because of its successful application in dimensionality reduction of data. To reduce the sensitivity of the theory to noise and data distribution in practical applications, the study of robust FRS model still attracts great attention. This research is devoted to the robust fuzzy rough uncertainty measure theory for multi-density data. Firstly, soft-neighborhood theory is combined with classical FRSs to design a generalized FRS model which is simply named SNFRS. The new model can effectively reduce the influence of noise and multi-density distribution on uncertainty measure of data. Secondly, with the SNFRS model, soft fuzzy rough indiscernibility theory is proposed, and it is used to design feature selection algorithms. In this research, a fully supervised feature selection and a semi-supervised feature selection algorithms are respectively proposed based on the soft fuzzy rough indiscernibility theory. Besides, the labeling method of the semi-supervised feature selection is also based on the theory. Finally, some experiments are performed to verify the proposed models and algorithms. The results show that the feature selection algorithms based on the soft fuzzy rough indiscernibility are feasible and efficient. This indirectly indicates that the FRS model based on soft-neighborhood is effective, successful and generalized in measuring uncertainty of data.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"513 ","pages":"Article 109397"},"PeriodicalIF":3.2,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The graph of a family of functions over quadratic extensions of finite fields

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-04-01 DOI: 10.1016/j.disc.2025.114500

Claude Gravel , Daniel Panario , Hugo Teixeira

{"title":"The graph of a family of functions over quadratic extensions of finite fields","authors":"Claude Gravel , Daniel Panario , Hugo Teixeira","doi":"10.1016/j.disc.2025.114500","DOIUrl":"10.1016/j.disc.2025.114500","url":null,"abstract":"<div><div>Brochero and Teixeira (2023) <span><span>[4]</span></span> showed the behavior of the functional graph of <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>q</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>a</mi><msup><mrow><mi>X</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> over quadratic extensions of finite fields explicitly for <span><math><mi>a</mi><mo>∈</mo><mo>{</mo><mn>1</mn><mo>,</mo><mo>−</mo><mn>1</mn><mo>}</mo></math></span>. In this article, we create a family of functions using repeated iterations of the function <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> and taking values of <span><math><mi>a</mi><mo>∈</mo><mo>{</mo><mn>1</mn><mo>,</mo><mo>−</mo><mn>1</mn><mo>}</mo></math></span> in each iteration. Let <em>α</em> be an <em>n</em>-sequence of values for <em>a</em>, taken over <span><math><mo>{</mo><mn>1</mn><mo>,</mo><mo>−</mo><mn>1</mn><mo>}</mo></math></span>, and <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> be the resulting function. We present the form of <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> and use it to derive a closed formula for the number and length of cycles present in the functional graph of <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span>. We then determine the shape of the trees hanging from each cycle and gather all the results in our main theorem.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 8","pages":"Article 114500"},"PeriodicalIF":0.7,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Global solutions to the higher-dimensional chemotaxis-consumption system

IF 1.2 3区数学

Journal of Mathematical Analysis and Applications Pub Date : 2025-04-01 DOI: 10.1016/j.jmaa.2025.129540

Wenping Du

引用次数: 0

A composition method for neat formulas of chromatic symmetric functions

IF 1 3区数学

Advances in Applied Mathematics Pub Date : 2025-04-01 DOI: 10.1016/j.aam.2025.102886

David G.L. Wang , James Z.F. Zhou

引用次数: 0

Generating Mandelbrot and Julia sets using PV iterative technique

IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2025-04-01 DOI: 10.1016/j.chaos.2025.116346

Pragati Gautam , Vineet

{"title":"Generating Mandelbrot and Julia sets using PV iterative technique","authors":"Pragati Gautam , Vineet","doi":"10.1016/j.chaos.2025.116346","DOIUrl":"10.1016/j.chaos.2025.116346","url":null,"abstract":"<div><div>In this study, we utilize the PV iteration method to generate Mandelbrot and Julia sets for the function <span><math><mrow><mi>G</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>z</mi></mrow><mrow><mi>k</mi></mrow></msup><mo>+</mo><mi>c</mi></mrow></math></span>. We establish escape criterion conditions for the PV iteration and provide a variety of graphical examples for different parameter settings. We also compare the graphs with those generated by other well-known iterations, such as the Picard-Mann and M iterations. Furthermore, we investigate the dependency between the iteration’s parameters and three numerical measures: the average escape time (AET), the non-escaping area index (NAI), and the fractal generation time. A comparative analysis is conducted with the renowned Mann, Picard-Mann, and M iteration methods. The results demonstrate that the fractals generated by the PV iteration exhibit distinct characteristics compared to those generated by other iterations, with non-linear dependencies that vary between different methods. These findings highlight the unique properties and potential applications of PV iteration in fractal generation.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116346"},"PeriodicalIF":5.3,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143746962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Synaptic delays shape dynamics and function in multimodal neural motifs.

IF 2.7 2区数学

Chaos Pub Date : 2025-04-01 DOI: 10.1063/5.0233640

Xinxin Qie, Jie Zang, Shenquan Liu, Andrey L Shilnikov

{"title":"Synaptic delays shape dynamics and function in multimodal neural motifs.","authors":"Xinxin Qie, Jie Zang, Shenquan Liu, Andrey L Shilnikov","doi":"10.1063/5.0233640","DOIUrl":"https://doi.org/10.1063/5.0233640","url":null,"abstract":"<p><p>In neuroscience, delayed synaptic activity plays a pivotal and pervasive role in influencing synchronization, oscillation, and information-processing properties of neural networks. In small rhythm-generating networks, such as central pattern generators (CPGs), time-delays may regulate and determine the stability and variability of rhythmic activity, enabling organisms to adapt to environmental changes, and coordinate diverse locomotion patterns in both function and dysfunction. Here, we examine the dynamics of a three-cell CPG model in which time-delays are introduced into reciprocally inhibitory synapses between constituent neurons. We employ computational analysis to investigate the multiplicity and robustness of various rhythms observed in such multi-modal neural networks. Our approach involves deriving exhaustive two-dimensional Poincaré return maps for phase-lags between constituent neurons, where stable fixed points and invariant curves correspond to various phase-locked and phase-slipping/jitter rhythms. These rhythms emerge and disappear through various local (saddle-node, torus) and non-local (homoclinic) bifurcations, highlighting the multi-functionality (modality) observed in such small neural networks with fast inhibitory synapses.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143763028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Machine-learning potential energy surfaces implications in photodissociation process.

IF 2.7 2区数学

Chaos Pub Date : 2025-04-01 DOI: 10.1063/5.0249690

Joaquin de la Cerda, Johan F Triana

{"title":"Machine-learning potential energy surfaces implications in photodissociation process.","authors":"Joaquin de la Cerda, Johan F Triana","doi":"10.1063/5.0249690","DOIUrl":"https://doi.org/10.1063/5.0249690","url":null,"abstract":"<p><p>Multi-state quantum molecular dynamics is one of the most accurate methodologies for predicting rates and yields of different chemical reactions. However, the generation of potential energy surfaces (PES), transition dipoles, and non-adiabatic couplings from ab initio calculations become a challenge, especially because of the exponential growth of computational cost as the number of electrons and molecular modes increases. Thus, machine learning (ML) emerges as a novel technique to compute molecular properties using fewer resources. Yet, the validity of ML methodologies continues in constant development, particularly for high-energy regions where conventional ab initio sampling is reduced. We test the accuracy of the potential energy surfaces interpolated with machine learning (ML) techniques in the solution of the time-dependent Schrödinger equation for the conventional IR+UV bond-breaking process of semi-heavy water. We perform a statistical analysis of the differences in expectation values and dissociation probabilities, which depend on the number of ab initio points selected to generate the machine learning potential energy surface (ML-PES). The energy differences of the electronic excited state modify population transfer from the ground state by driving with a UV laser pulse. We consider as the exact solution the photodynamics implemented with analytical expressions of the electronic ground X~1A1 and excited A~1B1 states. The results of the mean bond distance and dissociation probabilities suggest that ML-PES is suitable for dynamics calculations around the Franck-Condon region, and that standard interpolation methods are more efficient for multistate dynamics that involve dissociative and repulsive energy regions of the electronic states. Our work contributes to the continued inclusion of ML tools in molecular dynamics to obtain accurate predictions of dissociation yields with fewer computational resources and non-written rules to follow in multi-state dynamics calculations.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143762456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Interaction topology optimization by adjustment of edge weights to improve the consensus convergence and prolong the sampling period for a multi-agent system

IF 3.5 2区数学

Applied Mathematics and Computation Pub Date : 2025-04-01 DOI: 10.1016/j.amc.2025.129428

Tongyou Xu , Ying-Ying Tan , Shanshan Gao , Xuejuan Zhan

引用次数: 0

Aging in coevolving voter models

IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2025-04-01 DOI: 10.1016/j.chaos.2025.116344

Byungjoon Min , Maxi San Miguel

引用次数: 0

Temporal correlation-based neural relational inference for binary dynamics

IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2025-04-01 DOI: 10.1016/j.chaos.2025.116350

Haowei Zhang , Yuexing Han , Gouhei Tanaka , Bing Wang

{"title":"Temporal correlation-based neural relational inference for binary dynamics","authors":"Haowei Zhang , Yuexing Han , Gouhei Tanaka , Bing Wang","doi":"10.1016/j.chaos.2025.116350","DOIUrl":"10.1016/j.chaos.2025.116350","url":null,"abstract":"<div><div>Binary-state dynamics are prevalent in nature, from societal dynamics to dynamical systems in physics. Reconstructing a network structure behind interacting binary-state dynamical systems is essential, as it can facilitate understanding of these dynamical systems and improve the accuracy of predicting dynamical behavior. So far, few works have focused on correlation information in binary-state temporal data to help reconstruct networks. In this study, we propose temporal correlation-based neural relational inference for binary dynamics (TCNRI), inspired by the maximum likelihood estimation of activation events in binary dynamics processes. TCNRI constructs instantaneous correlation features and long-term correlation features by analyzing activation events in the time series data. These features capture the correlation information and help TCNRI reconstruct the network structure. We treat the binary-state dynamical process as a Markov process and use neural networks to reproduce node dynamics based on the reconstructed network structure. We conduct simulations on the classic susceptible–infected–susceptible (SIS) dynamics and Ising dynamics. The results show that TCNRI significantly outperforms baseline models and can accurately reconstruct the network structure for both typical synthetic networks and real networks.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116350"},"PeriodicalIF":5.3,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143746963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0